Employment restrictions on marriage were quite common (not only in teaching), and were logical when married women had no legal or financial status independent of their husbands, and therefore probably couldn't sign a contract of employment, or be paid for working.

If I correctly recall stories from my grandmother, along with books and movies, ice cream parlors of that time and location (mid-west, United States) functioned as a social gathering place for young adults: a place where young people could hang out, so to speak.

Unlike ice cream stores of today, where one (1) stands in line, (2) orders product, and (3) gets the hell out, ice cream parlors back then were a place for gathering for an extended period of time, socializing and mingling with other members of one's age group.

There's no particular "ill repute" about that. I'm guessing the teachers just weren't allowed to "hang-out" with gangs of youngsters.

[Edit: by the way, I was not able to find the original source of the material. The website quoted in the OP seems to have a quote reprinted from the Nebraska Farmer, September 1999, but the link appears to be broken.]

As for the particular restrictions on female teachers (assuming the authenticity of the document, which may be doubtful), I find it incredible just how much society has changed within a century with respect to female employment. I live in a day and age where it's perfectly normal for women to work in just about any profession -- to imagine a time not so long ago where women were effectively barred from most workplaces and didn't even have the right to vote is just mind-boggling to me.

Sounds a lot like the Arab countries today, just not quite as restrictive.

hmmm.... Haven't they been complaining about our "bad influence"?

...
Mashhad[Iran] is popular for its religious tourism and old bazaar (old market) where men and women shop together. Eating out is quite popular among the youth, with their first target being ice cream parlors. It is amazing to see that you will not find a cigar shop at every corner of the city, but you will definitely find an ice cream parlor, offering you dozens of flavors. When I asked my companion why there were so much ice cream parlors in the town, she smiled and said, “We are a sweet nation, and we like to eat sweets.”
...(ref)

Staff: Mentor

Here's some history from PBS.

"God seems to have made woman peculiarly suited to guide and develop the infant mind, and it seems...very poor policy to pay a man 20 or 22 dollars a month, for teaching children the ABCs, when a female could do the work more successfully at one third of the price." -- Littleton School Committee, Littleton, Massachusetts, 1849

Especially in big city schools, teachers at the turn of the 20th century felt like the most insignificant cogs in a huge machine. They felt dictated to and spied upon. Furthermore, they were badly paid and lacked pension benefits or job security. Many teaching positions were dispensed through political patronage. Married women were often barred from the classroom, and women with children were denied a place in schools. And daily conditions could be deplorable.

Sheila Hobbs Wilcox says . . . | September 16, 2013 / 7:48 pm
I worked in the Pupil Records Department of a public school district for many years. In the back of an old file cabinet I found student attendance books dated around 1895 to 1905. Several pages in the front of each book contained these same rules. The books are now part of the collection of the local museum. (ref)

Not sure if I ever mentioned the fact that I have a web page devoted to a certain brand of boat made in Gray's Harbor Washington, that ceased production in about 1960. I did a lot of web surfing to get a little bit of information. Later, I went to the library in Aberdeen, and found more information. Later on still, I went to the birthday party of the guy who built my boats. He, and his family, told me more than I can reveal.

Moral of the story?

Sometimes, you have to go to the library, and/or museum. And sometimes, well, let's just say they told me that grandpa* was found floating, face down, in Gray's Harbor one night, for no good reason.....

*Grandpa started the business in the early 40's. The guy who built my boats, was his son, and was 90 when I met him, in 2005.

Each school board, district, jurisdiction would have to have had local considerations, so being part of ' education history' from places such as Ontrario, Iowa, Alaska, New Zealand that have nothing to do with one another makes the listing dubious.